`sse_client` fails if URL is not on the root path

[michaelpoluektov]

Describe the bug
This line is the problem:

python-sdk/src/mcp/client/sse.py

Line 64 in babb477

endpoint_url = urljoin(url, sse.data)

urljoin discards the whole path, meaning that if url is http://localhost:8000/mcp/sse and sse.data is /messages/?session_id=123 we get endpoint_url == "http://localhost:8000/messages/?session_id=123" instead of http://localhost:8000/mcp/messages/?session_id=123

To Reproduce

• Launch an MCP server with SSE on a path different from the root of the application.

app = FastAPI()
mcp = FastMCP("my-mcp-server")
app.mount("/mcp", mcp.sse_app())

• Try to connect to it using sse_client as per the tutorial

Expected behavior

endpoint_url should contain the suffix of url with /sse stripped instead of the whole path being stripped.

[TheCulliganMan]

The setup is a bit strange here, but setting the sse_path and message_path in your FastMCP instantiation does allow for this behavior.

mcp = FastMCP(
    sse_path=f"/mcp/sse",
    message_path=f"/mcp/messages/",
)

python-sdk/src/mcp/server/fastmcp/server.py

Lines 75 to 76 in babb477

	sse_path: str = "/sse"
	message_path: str = "/messages/"